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Proof step 52 from proof pot-root-est (previous step)

2 * i = j * j + j0, j = sqrt(2 * i), 2 * i < (j + 1) ^ 2, 0 < i, 0 ≤ i, 4 ^ (i / 3) ≤ (2 * i) ^ sqrt(2 * i), 1024 ≤ i, j0 ≤ 2 * j, 0 ≤ j, 0 ≤ j0 ⊦ (2 * i) ^ j < ((j + 1) ^ 2) ^ j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 53:
⊦ 0 ≤ i ∧ 0 ≤ i0 ∧ 0 < j → (i ^ j < i0 ^ j ↔ i < i0)
Proof step 54:
2 * i = j * j + j0, j = sqrt(2 * i), 0 < i, 2 * i < (j + 1) ^ 2, 0 ≤ j0, 0 ≤ j, j0 ≤ 2 * j, 1024 ≤ i, 4 ^ (i / 3) ≤ (2 * i) ^ sqrt(2 * i), 0 ≤ i ⊦ (2 * i) ^ j < ((j + 1) ^ 2) ^ j, 0 ≤ 2 * i ∧ 0 ≤ (j + 1) ^ 2 ∧ 0 < j

Rule argument

spec: <toplevel> name: ls-pos-03 seq: ⊦ 0 ≤ i ∧ 0 ≤ i0 ∧ 0 < j → (i ^ j < i0 ^ j ↔ i < i0) subst: [i0, j, i] → [(j + 1) ^ 2, j, 2 * i] flags: <all paths>

Additional information

Used terms: (j + 1) ^ 2, j, 2 * i